Add about half of the dry ingredients to the wet mixture in the blender. Pulse to mix. Add remaining dry ingredients. Pulse just to mix somewhat, scraping the sides of the blender a few times. Do not over-blend; it's fine if dry flour remains visible.

Transfer doughnut batter to a large mixing bowl. Stir in any unblended dry ingredients. Cover with plastic wrap and chill for 30 minutes to allow dough to firm up slightly (or up to 1 hour if it still feels sticky).

Dust a work surface with flour. Scoop out one-quarter of dough and pat out to 1/2 inch thick. Dip a 3-inch doughnut cutter in flour and cut out as many rounds as possible (or, if you don't have a doughnut cutter, use a 3-inch round cutter, then dip a 1-inch cutter in flour and cut out centers).

Carefully press scraps together and cut out more rounds and centers. Repeat with remaining dough.

Combine the sugar and cinnamon in a shallow bowl and set aside.

Arrange a layer of paper towels on a plate. Add oil to a large, deep, wide saucepan or Dutch oven to a depth of 2 inches, leaving plenty of headroom. Attach a deep-frying thermometer to the pan. Heat oil over medium-high heat until it reaches 365°F. Adjust heat to maintain temperature as needed.

Slip a thin metal spatula under a doughnut ring and gently slide it into the oil. Repeat with a few more doughnut rings, but do not crowd the pan.

Fry doughnuts until puffed and a rich brown on first side (lift with a fork or slotted spoon to check), about 2 minutes. Carefully flip doughnuts using forks or slotted spoons and fry second side until richly browned, about 2 minutes. Using forks, transfer doughnuts from oil to paper towels.

Turn the warm doughnuts in cinnamon sugar to coat, then transfer to a cooling rack. Repeat frying step with remaining doughnuts and doughnut holes and coat them in cinnamon-sugar.

Serve doughnuts warm or let cool completely and store in airtight container at room temperature up to 2 days. Reheat gently in a 350°F oven before serving.